The paper introduces a new class of port‑Hamiltonian neural networks that can model systems with multiple asymptotically stable equilibria. By parameterizing the Hamiltonian as a product of Bregman divergences generated by an input‑convex network, the authors overcome the limitation of previous models that could only represent a single attractor. They prove local Lyapunov stability, show that additional non‑asymptotically stable equilibria must exist, and demonstrate improved convergence on three benchmark systems.
By Simon Heilig, Jens P\"uttschneider, Mohammad Itani, Asja Fischer, Timm Faulwasser
The paper introduces a structured method for learning linear operators in control systems using data. It leverages the framework of (semi)groups for evolution equations to establish structural assumptions and applies inverse‑problems theory to analyze learning algorithms, revealing error decompositions, convergence guarantees, and optimal regularization. Focusing on bounded operators on Hilbert spaces, the authors derive a convergent estimator for time‑varying systems, illustrating the practical power of their approach.
By Max Beier, Nicolas Hoischen, Sandra Hirche, Petar Bevanda
arXiv:2607. 00320v1 Announce Type: cross Abstract: We establish approximation and learning guarantees for Fourier neural operators (FNOs) applied to time-$T$ solution operators of dissipative evolution equations.
By Nisha Chandramoorthy, Daniel Sanz-Alonso, Nathan Waniorek
arXiv:2410.23667v2 Announce Type: replace
Abstract: Neural differential equations offer a powerful approach for learning dynamical systems from data. However, they do not inherently respect known con...
By Alistair White, Anna B\"uttner, Maximilian Gelbrecht, Valentin Duruisseaux, Niki Kilbertus, Frank Hellmann, Niklas Boers
Nonlinear GENERIC-Embedded Neural Networks (N-GENNs) are a deep learning framework designed to discover evolution equations for systems governed by the nonlinear GENERIC formalism. The method incorporates generalized gradient flows through convex dissipation potentials, allowing it to capture a wider range of thermodynamically consistent dynamics, including those with non‑quadratic dissipation potentials. Thermodynamic structure is enforced by construction, ensuring compliance with the first and second laws, and the approach is validated on a harmonic oscillator with a heat bath, an idealized chemical motor, and a one‑dimensional viscoplastic Perzyna model.
By Vojt\v{e}ch Votruba, Zequn He, Weilun Qiu, Celia Reina, Michal Pavelka
arXiv:2604. 19465v3 Announce Type: replace-cross Abstract: Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering.
By Chengyun Wang, Liwei Chen, Nils Thuerey
arXiv:2505. 15497v3 Announce Type: replace Abstract: Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems.
By Frederik Baymler Mathiesen, Nikolaus Vertovec, Francesco Fabiano, Luca Laurenti, Alessandro Abate
arXiv:2608.22112v1 Announce Type: cross
Abstract: We present a machine learning framework for identifying sparse, interpretable models of dynamical systems directly from time-series data. Our approac...
By Nibodh Boddupalli, Jeff Moehlis
arXiv:2506. 01226v3 Announce Type: replace-cross Abstract: We study parameterizations of stabilizing nonlinear policies for learning-based control.
By Nicholas H. Barbara, Ruigang Wang, Alexandre Megretski, Ian R. Manchester
arXiv:2606. 10596v1 Announce Type: cross Abstract: This work proves that an $n$-dimensional hybrid system can be embedded into an $m$-dimensional Euclidean space equipped with a continuous vector field on its embedded image whenever $m>2n$.
By Sangli Teng, Hang Liu, Koushil Sreenath
This work proves that an $n$-dimensional hybrid system can be embedded into an $m$-dimensional Euclidean space equipped with a continuous vector field on its embedded image whenever $m>2n$. This result suggests that an intrinsically discontinuous hybrid system generically admits a continuous extrinsic representation that is well-posed for differentiable optimization.
The paper proposes a new interpretable machine learning approach for discovering unknown nonlinear ordinary differential equations from a single state trajectory. It differs from existing methods by deriving its formulation from Functional Analysis and Operator Theory and by defining a cost function as an integral distance between functions rather than a discrete error sum. An incremental learning algorithm enables online updates, allowing simultaneous identification of both system dynamics and external time‑varying forces, with numerical examples illustrating its benefits.
By Seyyed Shaho Alaviani, Yongzhi Qu, Gregory W. Vogl